# Coming Events

## Seminar

Date/Time:
Monday, July 24, 2017 - 11:30 to 12:30
Venue:
SMS Seminal Hall
Speaker:
Rahul Kumar Singh
Affiliation:
HRI, Allahabad
Title:
Maximal surfaces, Born-Infeld solitons and Ramanujan's identities

Abstract: In the first part of the talk we discuss a different formulation for describing maximal surfaces in Lorentz-Minkowski space $\mathbb{L}^3:=(\mathbb{R}^3, dx^2+dy^2-dz^2)$ using the identification of $\mathbb{R}^3$ with $\mathbb{C}\times \mathbb{R}$. This description of maximal surfaces help us to give a different proof of the singular Bj\"orling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surfaces which contain a given closed real analytic spacelike curve and has a special singularity. In the next part we make an observation that the maximal surface equation and Born-Infeld equation (which arises in physics in the context of nonlinear electrodynamics) are related by a Wick rotation. We shall also show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. Finally in the last part of the talk we show the connection of maximal surfaces to analytic number theory through certain Ramanujan’s identities.

## Seminar

Date/Time:
Friday, August 4, 2017 - 15:30 to 16:30
Venue:
SMS Seminal Hall
Speaker:
Mr. Biswajit Rajaguru
Affiliation:
University of Kansas
Title:
Projective normality of line bundles of the type $K_X+\pi^*L$ on a ramified double covering $\pi:X\to S$ of an anticanonical rational surface $S$

Abstract:- Suppose $X$ is a minimal surface, which is a ramified double covering $\pi:X\to S$, of a rational surface $S$, with dim $|-K_S|\geq 1$. And suppose $L$ is a divisor on $S$, such that $L^2\geq 7$ and $L\cdot C\geq 3$ for any curve $C$ on $S$. Then the divisor $K_X+\pi^*L$ on $X$, is base-point free and the multiplication map in it's section ring : $Sym^r(H^0(K_X+\pi^*L))\to H^0(r(K_X+\pi^*L))$, is surjective for all $r\geq 1$. In particular this implies, when $S$ is also smooth and $L$ is an ample line bundle on $S$, that $K_X+n\pi^*L$ embeds $X$ as a projectively normal variety for all $n\geq 3$. In this talk we will present this result and various things associated to it.

## Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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